Question

Let f(x) = x-2 and g(x) = x^2-7x-9. Find f(g(-1))

Answer 1

\(\bf f(x) = x-2 \qquad {\color{brown}{ g(x)}} = x^2-7x-9
\\ \quad \\
f(\quad {\color{brown}{ g(x)}})=[{\color{brown}{ g(x)}}]-2\implies f(\quad {\color{brown}{ g(x)}})=[{\color{brown}{ x^2-7x-9}}]-2
\\ \quad \\
f(\quad {\color{brown}{ g({\color{blue}{ -1}})}})=[{\color{brown}{ ({\color{blue}{ -1}})^2-7({\color{blue}{ -1}})-9}}]-2\)

Answer 2

notice.... all you'd do is INSERT one function inside the other
so any "x" instances in f(x), get overtaken by g(x) which happen to be a trinomial